`BookProof.ChapterWignerSymmetry.sum_pairCoord` (b : OrthonormalBasis ι ℂ E) {o i : ι} (hi : i ≠ o) : ∑ j, pairCoord o i j • b j = b o + b i

Proved

BookProof.ChapterWignerSymmetry.sum_pairCoord

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerSymmetry.

BookProof.ChapterWignerSymmetry.sum_pairCoord (b : OrthonormalBasis ι ℂ E) {o i : ι} (hi : i ≠ o) : ∑ j, pairCoord o i j • b j = b o + b i

Formalization note: Lean 4 identifier BookProof.ChapterWignerSymmetry.sum_pairCoord.

Preamble

-- Generated from ChapterWignerSymmetry.lean — theorem BookProof.ChapterWignerSymmetry.sum_pairCoord
import Mathlib
import Definitions.Def_ChapterWignerSymmetry
open BookProof.ChapterWignerSymmetry


open scoped InnerProductSpace ComplexConjugate
open Finset


variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]


variable {T : E → E}

variable {ι : Type*} [Fintype ι] [DecidableEq ι]
variable {S : (ι → ℂ) → (ι → ℂ)} {o : ι}

Formal statement

theorem BookProof.ChapterWignerSymmetry.sum_pairCoord (b : OrthonormalBasis ι ℂ E) {o i : ι} (hi : i ≠ o) :
    ∑ j, pairCoord o i j • b j = b o + b i := by sorry

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